Complex Twinning, Polytypism and Disorder Phenomena in the Crystal Structures of Antimonpearceite and Arsenpolybasite

321

The Canadian Mineralogist Vol. 45, pp. 321-333 (2007)

COMPLEX TWINNING, POLYTYPISM AND DISORDER PHENOMENA IN THE CRYSTAL STRUCTURES OF ANTIMONPEARCEITE AND ARSENPOLYBASITE

Luca BINDI§

Museo di Storia Naturale, Sezione di Mineralogia, Università degli Studi di Firenze, via La Pira 4, I–50121 Firenze, Italy

Michel EVAIN

Laboratoire de Chimie des Solides, I.M.N., UMR C6502 CNRS – Université de Nantes, 2, rue de la Houssinière, BP 32229, F–44322 Nantes Cedex 3, France

Silvio MENCHETTI

Dipartimento di Scienze della Terra, Università degli Studi di Firenze, via La Pira 4, I–50121 Firenze, Italy Abstract

The crystal structures of antimonpearceite, arsenpolybasite-222 and arsenpolybasite-221 have been solved and refi ned from single-crystal X-ray-diffraction datasets. Antimonpearceite crystallizes in the trigonal space-group P¯3m1, with a 7.4805(5), c 11.8836(13) Å, V 575.89(8) Å3 and Z = 1. The refi nement of the structure leads to R = 0.0352 for 1095 independent observed refl ections [I/(I) ≥ 2] and 98 parameters. Arsenpolybasite-222 crystallizes in the monoclinic space-group C2/c, with a 26.036(2), b 15.0319(13), c 24.042(3) Å, 90.000(13)° (pseudohexagonal cell with the a = √3b orthohexagonal relation), V 9409.5(15) Å3 and Z = 16. A second-degree twinning by metric merohedry gives rise to an apparent trigonal symmetry, with the unit-cell parameters (hexagonal cell) a 15.0319(13) and c 24.042(3) Å. The refi nement of the structure leads to R = 0.0716 for 22008 independent observed refl ections [I/(I) ≥ 2] and 552 parameters. Arsenpolybasite-221 crystallizes in the space group P321, with a 14.9746(17), c 11.9982(6) Å, V 2330.0(4) Å3 and Z = 4. The refi nement of the structure, including a mirror-twin operation (fi rst- degree twin, ¯3'2/m'1 polychromatic point-group), leads to R = 0.0434 for 4639 independent observed refl ections [I/(I) ≥ 2] and 2– 2+ 184 parameters. All the structures consist of the stacking of [(Ag,Cu)6(As,Sb)2S7] and [Ag9CuS4] module layers along [001]; (As,Sb) forms isolated (As,Sb)S3 pyramids typically occurring in sulfosalts, copper links two sulfur atoms in a linear coordination, and silver occupies sites with coordination ranging from quasilinear to almost tetrahedral. The substitution of Cu for Ag in 2– the [(Ag,Cu)6(As,Sb)2S7] module layer becomes greater in going from the 111 structure, through the 221, to the 222 structure. The determination of the crystal structure for all the members of the group leads us to consider them as a family of polytypes. Keywords: antimonpearceite, arsenpolybasite, polytypism, disorder, twinning, crystal-structure determination. Sommaire

Nous avons résolu et affi né la structure cristalline de l’antimonpearceïte, l’arsenpolybasite-222 et l’arsenpolybasite-221 à partir de données en diffraction X prélevées sur monocristaux. L’antimonpearceïte cristallise dans le groupe spatial P¯3m1, système trigonal, avec a 7.4805(5), c 11.8836(13) Å, V 575.89(8) Å3 et Z = 1. L’affi nement de la structure a mené à un R égal à 0.0352 pour 1095 réfl exions indépendantes observées [I/(I) ≥ 2] et 98 paramètres. L’arsenpolybasite-222 cristallise dans le groupe spatial C2/c, système monoclinique, avec a 26.036(2), b 15.0319(13), c 24.042(3) Å, 90.000(13)° (maille pseudohex- agonale avec la relation orthohexagonale ayant la relation a = √3b), V 9409.5(15) Å3 et Z = 16. Une macle de second degré par méroédrie métrique produit une symétrie trigonale apparente, avec les paramètres réticulaires (maille hexagonale) a 15.0319(13) et c 24.042(3) Å. L’affi nement de la structure a mené à un R égal à 0.0716 pour 22008 réfl exions indépendantes observées [I/(I) ≥ 2] et 552 paramètres. L’arsenpolybasite-221 cristallise dans le groupe spatial P321, avec a 14.9746(17), c 11.9982(6) Å, V 2330.0(4) Å3 et Z = 4. L’affi nement de la structure, qui comprend une opération de macle mirroir (macle de premier degré, groupe ponctuel polychromatique ¯3'2/m'1), a mené à un R égal à 0.0434 pour 4639 réfl exions indépendantes observées [I/(I) 2– 2+ ≥ 2] et 184 paramètres. Ces trois structures sont faites d’un empilement de modules [(Ag,Cu)6(As,Sb)2S7] et [Ag9CuS4] en couches le long de [001]; le (As,Sb) forme des pyramides (As,Sb)S3 isolées typiques des sulfosels, avec le cuivre lié à deux atomes de soufre en coordinence linéaire, et les atomes d’argent en coordinence quasiment linéaire à tétraédrique. Avec une 2– substitution du Cu pour Ag, le volume du module en couche [(Ag,Cu)6(As,Sb)2S7] augmente de la structure 111 à la structure 221, et enfi n à la structure 222. La détermination de la structure des trois membres du groupe nous pousse à les considérer une famille de polytypes. Mots-clés: antimonpearceïte, arsenpolybasite, polytypisme, désordre, macles, détermination de la structure.

§ E-mail address: [email protected]ﬁ .it 322 the canadian mineralogist

Introduction Background Information

The minerals belonging to the pearceite–polybasite A summary of all known cell metrics and space group were divided by Frondel (1963) into two series: groups in the pearceite–polybasite group is given in the fi rst one, involving pearceite [(Ag,Cu)16(As,Sb)2S11] Table 1. To describe the complex electron-density and antimonpearceite [(Ag,Cu)16(Sb,As)2S11], is associated with Ag,Cu observed in these structures, characterized by a “small” unit-cell [labeled 111] Bindi et al. (2006a) and Evain et al. (2006a, b) used and a high Cu content; the second one, with poly- a non-harmonic model based upon a development of basite [(Ag,Cu)16(Sb,As)2S11] and arsenpolybasite the atomic displacement factor (Kuhs & Heger 1979, [(Ag,Cu)16(As,Sb)2S11], has doubled unit-cell param- Boucher et al. 1993, Evain et al. 1998). In general, in eters [labeled 222] and a low Cu content. Moreover, the the presence of atomic disorder, a split-atom approach existence of an intermediate type of unit cell, labeled is classically used in structure determinations. However, 221, was claimed for both polybasite (Harris et al. 1965, that approach has several disadvantages, and gives rise Edenharter et al. 1971) and arsenpolybasite (Minčeva- to ambiguities. As Bachmann & Schulz (1984) have Stefanova et al. 1979). From the crystallographic point demonstrated, the introduction of extra positions in the of view, these minerals were initially reported as being refi nement does not necessarily means that those posi- monoclinic C2/m, although dimensionally pseudo- tions correspond to occupied equilibrium sites. This is hexagonal (Peacock & Berry 1947, Frondel 1963, Harris particularly true in the case of fast ionic conductors, for et al. 1965, Hall 1967, Sugaki et al. 1983). Recently, which there exists a delocalization of an ionic species Bindi et al. (2006a) solved and refined the crystal over a liquid-like structure, and also where cations such structure of pearceite in the space group P¯3m1. They as a d10 element easily adopt a complicated coordination showed that the structure of pearceite can be described because of s,d orbital mixing or polarization factors as a regular alternation of two kinds of layer stacked (Gaudin et al. 2001). In addition to the problem of the along the c axis: a fi rst layer (labeled A), of general physical meaning of the refi ned positions, one usually 2– composition [(Ag,Cu)6(As,Sb)2S7] , and a second layer observes that the closer the refi ned positions in a disor- 2+ (labeled B), with a general composition [Ag9CuS4] . dered structure, the higher the correlations and the more The complex polytypism phenomena (i.e., 221 and unstable the refi nements. The use of tensor elements of 222 unit-cell types) occurring in various samples of higher order in the expression of the structure factors polybasite were studied by Evain et al. (2006a). These (the “non-harmonic approach”) is then an alternative authors solved and refi ned the crystal structure of both solution, giving an equivalent description (Kuhs 1992). polybasite-221 (space group P321) and polybasite-222 The benefi t of the latter description over the split-atom (space group C2/c), and proposed a possible mechanism model is an easier convergence of the refi nement as a regulating the stabilization of unit-cell type in these result of much lower correlations among the refi ned minerals. Finally, by means of a study of a crystal of parameters, as proven in many structure determinations Se-rich antimonpearceite (with 2.55 atoms per formula (see for instance the case of argyrodite: Boucher et al. unit Se), Evain et al. (2006b) investigated the structural 1993). In both cases, however, the refi ned coordinates role of selenium in these minerals. do not have a simple physical meaning, because they In this paper, we report the structural characteriza- are simply the fi rst-order terms in the expansion of the tion of the remaining members of the pearceite–poly- conventional structure-factor. Therefore, one must be basite group, antimonpearceite, arsenpolybasite-222 very cautious in interpreting bond distances from such and arsenpolybasite-221. refi nements. A better way to interpret the refi ned parameters is by using the joint probability-density function the crystal structures of antimonpearceite and arsenpolybasite 323

(jpdf), which can be directly calculated from the reﬁ ned As and Se, ±0.01 for Fe, Zn, Te, Au, Pb and Bi. The parameters. This function is the weighted superposition standards employed were: native elements for Cu, Ag, of the Fourier transform of the non-harmonic atom- Au, and Te, galena for Pb, pyrite for Fe and S, synthetic displacement factors of atoms over several sites. Sb2S3 for Sb, synthetic As2S3 for As, synthetic Bi2S3 for Bi, synthetic ZnS for Zn, and synthetic PtSe2 for Se. Occurrence and Chemical Composition The crystal fragments were found to be homogeneous within analytical error. The average chemical composi- The samples investigated, antimonpearceite (catalog tions (four to six analyses on each grain), together with number 171541, Smithsonian Institution, Washington), ranges of wt% of elements, are reported in Table 2. On arsenpolybasite-222 (catalog number AW634, Naturhis- the basis of 29 atoms, the formulae can be written as torisches Museum of Vienna) and arsenpolybasite-221 (Ag13.10Cu2.91Zn0.01Fe0.01)16.03(Sb1.73As0.17)1.90(S11.07 (catalog number AB6829, Naturhistorisches Museum of Te0.01)11.08, (Ag14.77Cu1.08Bi0.01Pb0.01Fe0.01Au0.01)15.89 Vienna), are from different localities: the Eagle mine, (As1.75Sb0.08)1.83(S11.23Te0.03)11.26 and (Ag14.64Cu1.55 Colorado, St. Joachimsthal (Bohemia), and Freiberg Zn0.01Bi0.02Au0.01)16.23(As1.76Sb0.01)1.77(S10.95Se0.01 (Germany), respectively. Te0.01)10.97 for the antimonpearceite, arsenpolybasite- A preliminary chemical analysis using energy- 222 and arsenpolybasite-221 crystals, respectively. It dispersive spectrometry, performed on the crystal frag- is worth noting that the sum (Sb + As) is considerably ments used for the structural study, did not indicate less than 2 in the chemical formulae; this feature could the presence of elements (Z > 9) other than S, Fe, Cu, be related to the sensitivity shown by these minerals to Zn, As, Se, Ag, Sb, Te, Au, Pb, and Bi. The chemical the electron beam. composition was then determined using wavelength- dispersive analysis (WDS) by means of a JEOL X-Ray Crystallography and Crystal- JXA–8200 electron microprobe. Concentrations of Structure Determination major and minor elements were determined at a 20 kV accelerating voltage and a 40 nA beam current, with 10 All the data collections were carried out on a s as counting time. For the WDS analyses, the following Bruker–Nonius Kappa CCD diffractometer using lines were used: SK, FeK, CuK, ZnK, AsL, graphite-monochromatized MoK–L2,3 radiation. In SeL, AgL, SbL, TeL, AuM, PbM, and BiM. expectation of possible twinning, special care was The estimated analytical precision (wt%) is: ±0.55 for taken with the choice of the fraction of reciprocal Ag, ±0.40 for Sb, ±0.30 for Cu, ±0.20 for S, ±0.05 for space covered. Intensity integration and standard 324 the canadian mineralogist

Lorentz-polarization correction were performed with refi nement are given in Table 3. Atom parameters are the Bruker–Nonius EvalCCD program package. Subse- reported in Tables 4, 5, and 6. quent calculations were conducted with the Jana2000 program suite (Petříček & Dušek 2000), except for Arsenpolybasite-222 the optimization of the crystal shape and dimension, which were performed with X-shape (Stoe & Cie 1996), The diffraction pattern of the arsenpolybasite- based on the Habitus program (Herrendorf 1993), and 222 crystal is apparently consistent with a trigonal the structure drawings, which were made with the symmetry, with the a and c parameters doubled (a program Diamond (Brandenburg 2001). Full-matrix ≈ 15.0, c ≈ 24.0 Å) compared to those of pearceite refi nements were carried out on F2, with all refl ections (a ≈ 7.4, c ≈ 11.8 Å; Bindi et al. 2006a). However, included. Tables of structure factors for these minerals taking into account the fi ndings of Evain et al. (2006a) are available from the Depository of Unpublished Data obtained for the structure of polybasite-222, after on the MAC web site [e.g., document antimonpearceite the correction for absorption by adopting a Gaussian CM45_321]. analytical method, the reflection dataset was trans- formed in the C-centered orthohexagonal cell and Antimonpearceite averaged accordingly, taking into account the twin law that makes the twin lattice (LT) hexagonal [twinning The study of the antimonpearceite crystal was made by metric merohedry: Nespolo (2004) and references slightly above room temperature (i.e., 330 K) to get therein]. It is worth noting that the only equivalent rid of visible diffuse lines related to the proximity of a refl ections of the twinned crystal are those related by the phase transition occurring just below 300 K (Bindi et al. inversion operation, as {E} and {i} are the only classes 2006b). The high temperature was achieved by means of 2/m that are complete classes of the fi rst-degree twin of an Oxford cryostream cooler. The diffraction pattern polychromatic point-group (Nespolo 2004): was found to be consistent with trigonal symmetry, with ()3 a ≈ 7.5 and c ≈ 11.9 Å. The sets of refl ections were ⎛ (,)21 ⎞ ()3 2 corrected for absorption with a Gaussian analytical κ ()3 = ⎜ ⎟ WB ⎜3 ⎟ method and averaged according to the point group 3¯m1 ⎝ m21, ⎠ (Rint = 0.0358). Starting from the model obtained for the structure of pearceite (Bindi et al. 2006a), the refi nement in the P3¯m1 space group converged smoothly to In the previous polychromatic symbol, elements that a residual R of 0.0352. To mimic the spread of elec- do not act as twin elements (achromatic elements) are trons associated with silver along diffusion paths, up indicated without chromatic index (none in the present to fourth-order non-harmonic Gram–Charlier tensors case), those that exchange all the individuals have one were used for the Debye–Waller description (Johnson chromatic index [(3) in the present case], and fi nally & Levy 1974, Kuhs 1984). Crystal characteristics, data those with partial chromaticity, which exchange a collection and reduction parameters, and results of the subset of the individuals and leave the other unchanged, are indicated with two chromatic indices [(2,1) in the the crystal structures of antimonpearceite and arsenpolybasite 325 326 the canadian mineralogist present case]. Finally, the global chromaticity, which polybasite-221 (Evain et al. 2006a). In this space group indicates the number of individuals (3 in the present and after the introduction of a mirror twin-operation case), is given as an external index. In our case, 2/m is (fi rst-degree twin, 6'2¯ m' Shubnikov K(2) dichromatic thus the eigensymmetry of the individual. point-group), the refinement smoothly converged Starting from the atom coordinates of polybasite-222 toward a residual R = 0.0434 value. The results are then (Evain et al. 2006a), the refi nement in space group C2/c only slightly improved (R = 0.0426) by the adjunction smoothly converged to R = 0.112 for observed refl ec- of the inversion twin-operation, yielding the following tions [2(I) level], including all the collected refl ections polychromatic point-group (Nespolo 2004): in the refi nement. At this point, the introduction of an additional twin-law with a two-fold axis, perpendicular ⎛ ⎞()4 622()222 () () to the previous three-fold axis, was tested as a generator κ()4 = ⎜ ⎟ twin-element, as it was used in the structure determina- ⎝ mmm()222 () ()⎠ tion of polybasite-222 (Evain et al. 2006a). It did not give signifi cant twin-volume ratios, and the additional twin-law was removed from the model. Crystal characteristics, data collection and reduction A non-harmonic approach with a Gram–Charlier parameters, and refinement results are gathered in development of the Debye–Waller factor up to the third Table 3. Atom parameters are reported in Tables 4, 5, order (Johnson & Levy 1974, Kuhs 1984) was then used and 6. to properly describe the electron density of two Ag atoms (i.e., Ag5, Ag9), in the vicinity of which residues were Description of the Structures found in the difference-Fourier synthesis maps. At the last stage, with anisotropic atom-displacement param- Basically, although not layered compounds, the eters for all atoms and no constraints other than full structures of antimonpearceite, arsenpolybasite-221 site-occupancy, the residual value settled at R = 0.0716 and -222 can be easily described as a regular alter- (Rw = 0.1441) for 22008 independent observed refl ec- nation of two kinds of layers stacked along [001]: a fi rst layer (labeled A or A’) with general composition tions [2 (I) level] and 552 parameters and at R = 0.1216 2– [(Ag,Cu)6(As,Sb)2S7] , and a second layer (labeled B (Rw = 0.1669) for all 32542 independent refl ections. 2+ Crystal characteristics, data collection and reduction or B’), with general composition [Ag9CuS4] . parameters, and refi nement results are given in Table 3. Atom parameters are reported in Tables 4, 5, and 6. Antimonpearceite

Arsenpolybasite-221 In the crystal structure of antimonpearceite (Fig. 1), (Sb,As) forms (Sb,As)S3 pyramids, as typically occur in As for the arsenpolybasite-222, the arsenpolybasite- 221 crystal system seems to be trigonal and could be indexed with a hexagonal cell (a ≈ 15.0, c ≈ 12.0 Å) related to that of antimonpearceite by the 2a 2b c relationship. After the usual Lorentz–polarization adjustment and a Gaussian analytical absorption-correction based upon optimized shape and dimension of the crystal, the structure reﬁ nement was carried out in space group P321 starting from the atom coordinates of the crystal structures of antimonpearceite and arsenpolybasite 327 sulfosalts, and copper links two sulfur atoms in a linear density-function (pdf) locations (modes) of diffusion- coordination. The silver cations are found in a fully like paths (i.e., Ag2 and Ag3). These positions corre- occupied position, labeled Ag1,Cu1, and in other two spond to low-coordination sites, in agreement with the sites corresponding to the most pronounced probability preference of silver for such environments (Table 7). In the A layer of the crystal structure of antimonpearceite, there occurs the only fully occupied position for the silver atoms. This fully occupied position, labeled (Ag1,Cu1), is triangularly coordinated by S atoms (two S2 and one S4), showing bond distances ranging from 2.464(2) to 2.465(2) Å, if the splitting of the S4 position is neglected in the calculation [see Bindi et al. (2006a) for an extensive description of the disorder]. The average bond-distance, 2.465 Å, is in agreement with a partial substitution of copper for silver at this site. The (Sb,As)S3 trigonal pyramids are isolated from 328 the canadian mineralogist each other, but linked to (Ag1,Cu1)S3 units to consti- The coordinations of the other silver positions are tute a layer and not a three-dimensional structure as in similar to those reported for the crystal structure of Cu12Sb4S13 (Pﬁ tzner et al. 1997). pearceite (Bindi et al. 2006a). Note that the Cu2 position shows a linear coordination with two distances at 2.158(1) Å. Although these values are shorter than that found by the sum of ionic radii (i.e., 2.30 Å: Shannon 1981), they are in perfect agreement with those found in KCuS (2.129 and 2.162 Å: Savelsberg & Schäfer 1978), in which Cu2 shows a similar linear coordination with sulfur, which was explained through band-structure calculations by Gaudin et al. (2001).

Arsenpolybasite-222

The crystal structure of arsenpolybasite-222 (Fig. 2) can be seen as a succession along the c axis of two 2– module layers: the [(Ag,Cu)6Sb2S7] A (or A’) module 2+ layer and the [Ag9CuS4] B (or B’) module layer (A,B and A’,B’ being related by a c glide mirror operation of symmetry). 2– In the [(Ag,Cu)6Sb2S7] A (or A’) module layer, each silver cation has a three-fold coordination with sulfur. Out of the 12 independent Ag atoms of the A module layer, Ag3, Ag5 and Ag9 exhibit shorter distances (2.460, 2.465 and 2.498 Å, respectively). This structural feature indicates a partial replacement of 3– silver by copper at these particular sites. In the [AsS3] pyramids, the overall mean As–S bond distance [2.266 Å] is consistent with the value observed in the crystal structure of proustite, Ag3[AsS3] (2.293 Å, Engel & Nowacki 1966).

Fig. 1. Projection of the antimonpearceite structure along the a axis (hexagonal symmetry), emphasizing the succession 2– 2+ of the [(Ag,Cu)6Sb2S7] A (A’) and [Ag9CuS4] B (B’) module layers. the crystal structures of antimonpearceite and arsenpolybasite 329

Fig. 2. Projection of the arsenpolybasite-222 structure along the b axis (monoclinic sym- 2– 2+ metry), emphasizing the succession of the [(Ag,Cu)6Sb2S7] A (A’) and [Ag9CuS4] B (B’) module layers. 330 the canadian mineralogist

2+ In the [Ag9CuS4] B (or B’) module layer, the is equivalent to 222 = 2.159 Å. We also found 18 independent Ag atoms adopt various coordina- two silver atoms (i.e., Ag6 and Ag9) in a quasi-linear tions extending from quasi-linear to quasi-tetrahedral coordination [221 = 2.43 Å versus 222 (Table 8). In detail, seven silver atoms (i.e., Ag13, Ag15, Ag19, Ag21, Ag22, Ag23 and Ag28) can be considered in linear coordination with an overall mean Ag–S of 2.43 Å, although the S–Ag–S angles invari- ably depart from 180°. Six Ag atoms (i.e., Ag18, Ag24, Ag25 Ag27, Ag29, and Ag30) may be considered as three-fold coordinated, even though some of them are in an environment of two short bonds + one long bond (Table 8). Taking into account three bonds per atom, an overall mean Ag–S of 2.59 Å can be calculated, in good agreement with both that found for the Ag(1) position in the crystal structure of stephanite, Ag5[S|SbS3] (2.54 Å: Ribár & Nowacki 1970) and that found for the Ag position in the crystal structure of pyrargyrite, Ag3[SbS3] (2.573 Å: Engel & Nowacki 1966). The last ﬁ ve silver atoms (i.e., Ag14, Ag16, Ag17, Ag20, Ag26) adopt a close-to-tetrahedral coordination. Once again, taking only four bonds for the averaging, one calculates an overall mean Ag–S = 2.71 Å, which matches that found for the Ag(3) position in the crystal structure of stephanite, Ag5[S|SbS3] (2.68 Å: Ribár & Nowacki 1970). Finally, the three copper atoms exhibit a nearly perfect linear coordination, with similar Cu–S distances [overall mean Cu–S = 2.159 Å]. The shortest cation–cation distances are: Ag–Cu: 2.7861(16) Å, Ag–Ag: 3.0016(15) Å, Ag–As : 3.377(2) Å.

Arsenpolybasite-221

The structure of 221-polybasite (Fig. 3) is obtained from the 222-polybasite structure by selecting half its cell content along the c axis, that is, either the A–B (or A’–B’) double-module layer or the A/2–B–A’/2 (or A’/2–B’–A/2) double-module layer, since A and A’ approximately correspond to each other by a ½ transla- tion along the c axis. The observed metal–sulfur distances compare well with those obtained for the 222-polybasite structure (Tables 8, 9). For instance, 221 = 2.264 Å matches the 222 = 2.266 Å value. Similarly, in 2+ the [Ag9CuS4] B module layer, 221 = 2.161 Å the crystal structures of antimonpearceite and arsenpolybasite 331

Fig. 3. Projection of the arsenpolybasite-221 structure along the a axis (hexagonal sym- 2– 2+ metry), emphasizing the succession of the [(Ag,Cu)6Sb2S7] A (A’) and [Ag9CuS4] B (B’) module layers.

= 2.43 Å], three silver atoms (Ag7, Ag8 and Ag10) in considered to be the correct space-group and why the a close to triangular coordination [221 = 2.60 structure could not be solved until now. Å versus 222 = 2.59 Å], and fi nally a silver The 222 structures show the –AB–A’B’–AB–A’B’– atom (Ag5) in approximately a tetrahedral coordina- double-layer module sequence (present study, Evain et tion [221 = 2.71 Å versus 222 = 2.71 al. 2006a); thus they can be considered as polytypes of Å]. The shortest cation–cation distances are: Ag–Cu: the 221 structures with sequence –AB–AB– (present 2.794(2) Å, Ag–Ag: 3.001(2) Å, Ag–Sb: 3.4693(19) Å. study, Evain et al. 2006a), the A’B’ double-layer module The good match between the arsenpolybasite-222 and being related to AB by a glide refl ection perpendicular arsenpolybasite-221 structures is illustrated in Figures to the b axis with translational component c/2. However, 4a and 4b. the AB221 module is not strictly equivalent in chemical composition to the AB222 (or A’B’222) module, the 221 Discussion structures being richer in copper (present study, Evain et al. 2006a). It seems that the higher the Cu content, the The crystal structures of antimonpearceite, arsen- more likely is the structure to be of the 221 type. As is polybasite-221 and arsenpolybasite-222 have been generally the case, the higher the disorder, the higher the solved and refi ned from single-crystal X-ray-diffraction apparent symmetry. With a limited substitution of Cu data. As already observed for polybasite-222 (Evain et for Ag, the crystal system is monoclinic with a double al. 2006a), the complexity of the determination of the c period (i.e., 222 structures). However, the AB (A’B’) arsenpolybasite-222 structure comes from the apparent double-layer module has a pseudotrigonal symmetry, trigonal symmetry linked to a second-degree twinning which explains the twinning and the apparent hexagonal by metric merohedry of the real monoclinic structure. It cell. By increasing the extent of the substitution of Cu should be stressed that in both the arsenpolybasite-222 for Ag, the cell doubling along the c direction is lost, and polybasite-222 structures, all the atom positions, and the average symmetry becomes trigonal (i.e., 221 2+ except those of the Ag atoms in the [Ag9CuS4] B structures). A further increase of the disorder gives rise pseudo layer, approximately follow a mirror (m[010]) to a folding of the cell along the a and b directions, as symmetry operation. Therefore, through the combina- found in the 111 structures (present study, Bindi et al. tion with the c glide-mirror symmetry operation of the 2006a). Our fi ndings support the idea of Hall (1967), C2/c space group, they are approximately translated by who suggested that the variation of Cu content in ½ along the c axis. This feature, along with the absence different samples might be the driving force of different of the h0l, l = 2n + 1 systematic extinction because of unit-cell stabilizations. the twinning, could explain why C2/m was mistakenly 332 the canadian mineralogist

Fig. 4. Superposition, down the c axis, of equivalent fractions of the [(Ag,Cu)6 2– 2+ (As,Sb)2S7] A (a) and [Ag9CuS4] B (b) module layers of arsenpolybasite-222 and arsenpolybasite-221, showing the good match between the two structures.

In summary, we found that the minerals of the Acknowledgements pearceite–polybasite group exhibit three types of unit cell (i.e., 111, 222, and 221) that correspond to three The authors are grateful to Prof. Paul G. Spry (Iowa separate structures (space group P3¯m1, P321, and C2/c State University, Ames, Iowa) for his help with the for 111, 221, and 222, respectively). The determination electron-microprobe analyses. The paper benefitted of the crystal structures of all the members of the group from the ofﬁ cial reviews made by Andrew Locock and allows to consider them as a family of polytypes, since an anonymous reviewer. The authors are also grateful to they are built up of layers of nearly identical structure Robert F. Martin for his suggestions on improving the and composition stacked along the c axis. For this manuscript. This work was funded by C.N.R. (Istituto reason, a proposal to change the existing nomenclature di Geoscienze e Georisorse, sezione di Firenze) and has been submitted to the IMA–CNMNC. by M.I.U.R., P.R.I.N. 2005 project “Complexity in minerals: modulation, modularity, structural disorder”. the crystal structures of antimonpearceite and arsenpolybasite 333

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